Trigonometry problem (need answer fast)

cos(x+y)cos(x-y) = cos^2x-sin^2y

Kind of confused about this one. First best answer gets 10 points!

cos(x+y)cos(x-y)

= (cos.cosy - sinx.siny)(cos.cosy + sinx.siny)

= cos^2x.cos^2y - sin^2x.sin^2y

= cos^2x.(1-sin^2y) - (1-cos^2x).sin^2y

= cos^2x - cos^2x.sin^2y - sin^2y + cos^2x.sin^2y

= cos^2x - sin^2y

L.H.S
=(cosx.cosy-sinx.siny) (cosx.cosy+sinx.siny)
=cosx.cosy(cosx.cosy+sinx.siny)-sinx.s…
=cos^2x.cos^2y+sinx.siny.cosx.cosy-sin…
=cos^2x.cos^2y-sin^2x.sin^2y
=cos^2x(1-2sin^2x)-(1-2cos^2x).sin^2y
=cos^2x-2sin^2x.cos^2x-sin^2y+2sin^2x.…
=cos^2x-sin^2y


R.S.H Proved

cos(x+y)cos(x-y) = cos^2(x)-sin^2(y)

1. [cos(x)cos(y)-sin(x)sin(y)] - [(cos(x)cos(y)-sin(x)sin(y)]

2. [(cos(x)cos(y)]^2 - [(sin(x)sin(y)]^2

3. cos^2(x)cos^2(y) - sin^2(x)sin^2(y)

4. cos^2(x) [1-sin^2(y)] - [1-cos^2(x)] sin^2(y)

5.cos^2(x) - [cos^2(x)sin^2(y)] - sin^2(y) + [cos^2(x)sin^2(y)]

6.cos^2(x) - sin^2(y)